Turing complete sets of game components with divinatory elements

ABSTRACT

One embodiment of a Turing complete set of game components in the form of a deck of playing cards, each card ( 110 ) having at least one divinatory element illustrated on its playing face ( 112 ). In other embodiments, the game components may take other forms, including, but not limited to components for board, dice or tile games. Additionally, the game components may be simulated in different types of non physical ways, including, but not limited to electronic games, video games, computer games, or interactive network games. The embodiments described and shown have the advantage over prior art of being able to simulate a universal Turing machine in a two player game for a finite period of time within a finite volume of space, which is sometimes referred to as a tabletop game.

BACKGROUND Prior Art

The following is a tabulation of some of the prior art that presentlyappears relevant:

U.S. Patents Patent Number Issue Date Patentee U.S. Pat. No. 2,383,0811945 Aug. 21 Ribbe U.S. Pat. No. 5,662,332 1997 Sep. 08 Garfield U.S.Pat. No. 5,843,661 1998 Dec. 01 Rothemund

NON-PATENT LITERATURE DOCUMENTS

-   CHURCHILL, ALEX. “Magic: the Gathering is Turing Complete.”    Toothycat. n.d. n. pag. Version 5. Web. Archived at    webcitation.org/6lyNqOClx on 18 Aug. 2013-   GOPINATH, RAHUL, et al. “Computing With Tiles.” Google Code. n.d. n.    pag. Web. Archived at webcitation.org/6lyEkOfCg on 18 Aug. 2013-   GOUCHER, A. P. “3D chess is Turing-complete” Complex Projective    4-Space. 5 Apr. 2013n. pag. Web. Archived at    webcitation.org/6lyDr73z6 on 18 Aug. 2013-   GRAY, JAMES W. “Magic 1513: Tarot Combat II.” Recoculous. 27 Mar.    2013 n. pag. Web. Archived at webcitation.org/6lyJoZCyj on 18 Aug.    2013-   KAISER, DAVID M. “Games are Turing Complete.” Mdc.edu. November    2003 n. pag. Web. Archived at webcitation.org/6JdU4W2H2 on 14 Sep.    2013-   KAYE, RICHARD “Infinite versions of minesweeper are Turing    complete.” University of Birmingham School of Mathematics. 31 May    2007 pp. 1-15 Web. Archived at webcitation.org/6lyMn8RwL on 18 Aug.    2013-   ROBINSON, KAREN D. “Playing Card Magic.” and “Wizard's Tower.”    Angelfire. n.d. n. pag. Web. Archived at webcitation.org/6lyDStacB    on 18 Aug. 2013-   ROGOZHIN, YURII. “Small universal Turing machines.” Theoretical    Computer Science. 20 Nov. 1996 pp. 215-40 vol. 168. issue 2.    Elsevier. Amsterdam, The Netherlands

Many different games and systems have been shown to be Turing completeor, in other words, equivalent to universal Turing machines (UTMs). Afew examples include:

-   -   an infinite variation of Minesweeper (Kaye)    -   3 dimensional chess with one dimension extending infinitely        (Goucher)    -   Wang tiles (Gopinath et al.)    -   John Conway's Game of Life (Gardner)

However, to my knowledge only one game playable on a finite playingsurface or within a finite volume of space (sometimes referred to as atabletop game) is currently claimed to be Turing complete—Magic: TheGathering—also known as MTG. (CHURCHILL, Magic: The Gathering is TuringComplete.).

‘I think it's the first demonstration of Turing completeness in therules of any tabletop game. I don't think there are any other boardgames or card games whose rules accommodate the complexity required tomake a Turing machine (and I've played a few hundred).’ Alex Churchill(CHURCHILL et al.)

It appears possible to discover one or more combinations of multiple MTGcards which when played in certain specific combinations by severalplayers will lead to the implementation of a universal Turing machinewithin MTG. However, so far it appears as though such an implementationwould require roughly 70 cards with 20 or more different names, playedby 4 or more different players in a precise order. Considering thatthere are many thousands of MTG cards available for each individualplayer to choose from in constructing a MTG card deck, the odds againstactually simulating a UTM during the course of a game would beastronomical.

In the past, games which have been shown to be Turing complete have haddisadvantages in terms of playability in one or more of the followingways:

-   -   a. most (Conway's Life, Wang tiles, 3D chess, infinite        Minesweeper) of the above listed games aren't tabletop games, as        they require one or more infinite dimension    -   b. many (Conway's Life, Wang tiles, infinite Minesweeper) are 0        or 1 player games, which are more akin to logical puzzles than        to games    -   c. implementation of a UTM within the tabletop game MTG is        extremely complex, requires many players, and would be rare in        actual play    -   d. no known game between only two players which can be played        within a finite surface area or volume is able to approximate a        UTM in the manner demonstrated with Magic: The Gathering

Therefore, described in detail below is one embodiment of a set of gamecomponents in the form of playing cards (110) which can be used to playa variety of games, including two player games. The cards (110) aredesigned as a set to simuate a UTM in certain game conditions for apredetermined finite length of time. By halting UTM calculations after afinite length of time, we truncate some calculations which would havehalted naturally given more time and we also halt some calculationswhich would not have halted otherwise. In the embodiment describedherein, Yurii Rogozhin's 4 state 6 color UTM (ROGOZHIN, 1996)instructions are used (FIG. 9C), but in other embodiments, differentUTMs may be used. Also, in other embodiments the game components mayresemble chess pieces (1018) or may take the form of other board gamepieces which have round or polygonal shapes with different numbers ofsides, either within the same set or different numbers of sides indifferent embodiments. Tiles, dominoes, or dice with various numbers ofsides are other potential embodiments for the game components.Additionally, the game components may be replicated or embodied in otherforms or media, for example as electronic games, video games, orcomputer games. The triggering of the UTM aspect as part of the play ofa game can be more or less of a strategic factor to be considered duringthe play of the game, depending on the rules of the particular gamechosen. Additionally, the game pieces may contain, be marked with, or beassociated with one or more fortune telling or divinatory symbols orelements. Briefly described below is some of the history linking gamesand fortune telling or divination.

Both divination by casting dice (Astragalomancy) and games which involvethe casting of dice like Backgammon have been practiced or played forthousands of years in countries throughout the world. In more recenttimes, both tarot and standard playing card decks have been used forrecreational game purposes as well as for divination purposes. Wim vanBinsbergen has made a comparison between the Mancala family of boardgames and the method of divination known as geomancy. Therefore, thecomplete history of recreational games and methods of divination wouldlikely fill several books and the earliest parts of that history willlikely continue to remain somewhat shrouded in mystery.

In the more modern history of divination and games, we find many patentresults for a patent search of “fortune telling” AND game. Many patentedfortune telling games, however, have as a primary goal or purpose ofplaying the game amusing or entertaining one or more players via a novelmethod of fortune telling or divination. As an example, in the rules forOracle Card Game by R. Ribbe the patent states: “The player or dealer issupposed to concentrate upon the subject on which information orprediction is desired” and “The object of the invention is to provide anovel form of amusement, which may be played as solitaire or for groupdiversion.” (Ribbe, U.S. Pat. No. 2,383,081) While each playing card(110) or game component described herein may contain one or more fortunetelling (divinatory) elements or symbols, the game components differfrom the above mentioned example as follows:

-   -   the rules and goals for games which may be played with the game        components will vary, but in general the primary goal of the        game will not be divination    -   divinatory meanings of cards may change during play of the game,        for example a tarot card (132, 734, 735, 946) or I Ching lines        (956, 960, 962, 164) may be interpreted differently when in an        upside down orientation    -   divinatory elements or symbols may alter attributes (190) of the        cards they appear on, for example a card's associated star (176,        178) may add power, toughness, and/or speed (190) to that card        when the turn number of the game matches that star's (176, 178)        lunar mansion (180)

SUMMARY

Sets of game playing components with divinatory elements which are ableto function as universal Turing machines. In one embodiment, a set ofgame playing cards (110) which under certain game conditions willsimulate Rogozhin's (4,6) universal Turing machine (FIG. 9 c).

ADVANTAGES

Accordingly, several advantages of one or more aspects are as follows:to allow the playing of tabletop Turing complete games including twoplayer games, to make the simulation of a UTM within the framework ofvarious games a strategic factor for consideration, to simplify thesimulation of a UTM within the framework of a tabletop game, to adddivinatory aspects to game components without making divination theprimary object or goal of using the game components, and to allowdivinatory elements to change or be changed by the play of the game.More advantages of one or more aspects will become apparent throughconsideration of the drawings and ensuing description.

DRAWINGS Figures

In the drawings, related figures have the same number, but differentalphabetic suffixes. The patent or application file contains at leastone drawing executed in color. Copies of this patent or patentapplication publication with color drawing(s) will be provided by theOffice upon request and payment of the necessary fee.

FIGS. 1A and B illustrate various aspects of two cards from the relatedclubs and wands suits.

FIGS. 2 A and B illustrate aspects of two cards from the related diamondand pentacles suits.

FIGS. 3 A and B illustrate aspects of two cards from the related heartsand cups suits.

FIGS. 4 A and B illustrate various aspects of two cards from the relatedspades and swords suits.

FIGS. 5 A and B illustrate various aspects of two cards of theC(hevalier) rank from the tarot portion of the deck.

FIGS. 6 A and B illustrate various aspects of the black and red jokersfrom the poker portion of the deck.

FIGS. 7 A and B illustrate various aspects of the Tower and Judgementcards from the tarot portion of the deck.

FIGS. 8 A and B illustrate various aspects of the Death and Justicecards from the tarot portion of the deck.

FIGS. 9 A, B, and C are reference tables which indicate how differentsymbols and elements have been assigned to the cards in the deck.

FIG. 10 illustrates a chessboard and chess pieces and some ways in whichUTM and divinatory elements can be assigned to them.

Drawings-Reference Numerals  110 playing card  112 playing face of card 114 UTM standard RGB color indicator symbol  516 standard RGB colorblue (0, 0, 255)  118 standard RGB color red (255, 0, 0)  220 standardRGB color green (0, 255, 0)  322 standard RGB color aqua (0, 255, 255) 424 standard RGB color yellow (255, 255, 0)  626 standard RGB colormagenta (255, 0, 255)  928 card rank  130 poker card rank  132 MinorArcana (GRAY, E. p. 1) card rank  734 Major Arcana (tarot trump) cardrank  735 Major Arcana card name  936 suit P(oker) (4 suits)  137 rankcolor - B(lack)  138 poker card suit - clubs  239 rank color - R(eddish) 240 poker card suit - diamonds  342 poker card suit - hearts  444 pokercard suit - spades  946 suit T(arot) (5 suits)  747 tarot card suit -trump  148 tarot card suit - wands  250 tarot card suit - pentacles  352tarot card suit - cups  454 tarot card suit - swords  956 I Ching (4different numbers of lines)  958 I Ching - line  960 I Ching - bigram 762 I Ching - trigram  164 I Ching - hexagram  168 alphabet letter -Greek  170 alphabet letter - Arabic  772 alphabet letter - Phoenician 174 alphabet letter (numerical value of)  176 star name  178 Bayerdesignation of star  180 Arabic lunar mansion  982 card cost (3 costtypes)  184 cost - rank color B  286 cost - rank color R  788 cost -either rank color  190 P(ower)/T(oughness)/S(peed) attributes  791arrow - forces next event/symbol  192 illustration  793 planetary symbol 194 flavor text  696 UTM color/symbol instruction box  897 new moonsymbol (state 1)  798 first quarter moon symbol (state 2)  699 full moonsymbol (state 3) 6100 last quarter moon symbol (state 4) 7101 moveL(eft) 7102 move R(ight) 6103 halt 7104 written/symbolic UTMinstructions 7105 Tower symbol 7106 Judgement symbol 7107 Musterillustration and instruction 8108 Death symbol 8109 Justice symbol 7110written text UTM related instructions 7111 Inspection - UTM read/writehead 8112 written UTM halt instruction 1010 chessboard 1012 playingsurface of chessboard 1014 white square 1016 black square 1018 chesspieces 1020 white rook 1022 white knight 1024 white bishop 1026 whiteking 1028 white queen 1030 white pawn 1032 black rook 1034 black knight1036 black bis hop 1038 black king 1040 black queen 1042 black pawn 1044chess piece cost/value

DETAILED DESCRIPTION FIGS. 1A-9C-First Embodiment

One embodiment of a Turing complete set of game components is a deck ofplaying cards (110) as described in detail herein. However, differentarrangements of divinatory elements (956, 168, 170, 772, 973, 174, 176,178, 180) on the playing faces (112) of the cards (110) are alsopossible and additional divinatory elements may be included in otherembodiments. Additionally, in other embodiments, sets of playing cards(110) may differ in other ways, for example in card rank (130, 132,734), card suit (936, 138, 240, 342, 444, 946, 747, 148, 250, 352, 454),card cost (982, 184, 286, 788), standard RGB colors (114, 516, 118, 220,322, 424, 626), flavor text (194), illustrations (192), or number ofplaying cards (110) in the set.

In the embodiment described herein, the deck of playing cards (110)consists of 132 cards in total, grouped as follows: a regular orstandard 52 card pack or deck (HOYLE pp. 1-2) of playing cards (130,936, 138, 240, 342, 444) modified as described below, two modifiedjokers designated as B (FIG. 6A) and R (FIG. 6B), and a 78 card tarotdeck (GRAY, E. pp. 13-145) (132, 734, 735, 946, 747, 148, 250, 352, 454)modified as described in detail below. The tarot cards (132, 734, 735,946, 747, 148, 250, 352, 454) generally follow the order and namingconventions used in A. E. Waite's Rider tarot deck (GRAY, E. pp. 3, 9,18ff) with some exceptions, such as leaving the word “The” out of trumpsuit card names (735) and using the card ranks (132) of J and C (FIGS.5A and 5B) instead of Page and Knight for a closer overallcorrespondence between the standard poker card (130) and tarot card(132) sections of the deck. All of the playing cards (110) will bemanufactured to have indistinguishable but not symmetrical designs ontheir reverse sides (not shown) so that when any playing card (110) isin a face down position it has right side up and upside downorientations, but cannot be distinguished from other cards (110) in thedeck.

The playing cards (110) are modified from their more familiarpredecessors with the addition of divinatory elements (956, 168, 170,772, 973, 174, 176, 178, 180), standard RGB colors (114, 516, 118, 220,322, 424, 626), flavor text (194), illustrations (192), tarot card suit(946) symbols (747, 148, 250, 352, 454) and other elements as may beseen more clearly in FIGS. 1A-9C.

FIG. 1A illustrates the Ace of clubs card. In the upper left corner ofthe playing face (112) of the card (110) is the universal Turing machinecolor indicator symbol (114). With the exception of the jokers (FIGS. 6Aand 6B) this will be the standard general location for the UTM colorindicator symbol (114). This symbol will be found on all of the cards,but will vary in rotational orientation and colors used. In this case,the indicated color is standard RGB red (118) which FIG. 1A shares incommon with FIG. 1B. Additionally, FIGS. 1A and 1B have in common therank color B (137). This is due to the poker clubs card suit (138)corresponding to the tarot wands card suit (148). The full list ofcorrespondences between cards of the same rank in the poker and tarotportions of the deck is illustrated in FIG. 9A.

Below the UTM standard RGB color symbol indicator (114) on FIG. 1A wehave, in descending order, the poker card rank A(ce) (130), the clubssuit symbol (138), the I Ching hexagram (164) for this card, a Greekalphabet letter (168)—α and its numerical value (174)—one, followed by astar name (176)—Sheratan, its Bayer designation (178)—β Aries, and itsArabic lunar mansion (180)—1st. In the corresponding locations on FIG.1B are the Minor Arcana card rank (132)—5, the tarot card suit symbolfor wands (148), the I Ching hexagram (164) for the 5 of Wands, thenumerical value (174)—ten—of the Arabic alphabet letter (170)

followed by a star name (176)—Zosma—and its Bayer designation (178)—δLeo—and the Arabic lunar mansion (180) for the star Zosma. In general,the placement of the above mentioned elements will remain consistentthroughout the poker card ranks (130) and suits (936) with the exceptionof the B and R Joker cards (FIGS. 6A and 6B). Similarly, the elementslisted above from FIG. 1B will be located in similar positions on theplaying faces (112) of the Minor Arcana (132, 946, 148, 250, 352, 454)of the tarot portion of the deck. Due to illustrations (192) of varyingdimensions, other elements may be located in somewhat differentlocations on the playing faces (112) of different cards (110).

When flavor text (194) is included on a card, as it is in both FIGS. 1Aand 1B, it will be distinguished from other types of text like writtenUTM instructions (7104) by being enclosed in parentheses. The generallocation of flavor text (194) on the playing face (112) of a card (110)will be centered directly below the illustration (192). The illustration(192) will be located in the upper center of the playing face (112) ofeach card (110) and extend downward toward the bottom of the card as faras needed for each particular illustration. Examples of different sizedillustrations (192) and how they affect the location of flavor text(194) on the playing face (112) of each card (110) may be seen bycomparing FIGS. 1A and 1B.

Finally, on the playing faces (112) illustrated in FIGS. 1A and 1B, wesee the card cost (184) and its power, toughness and speed indicator(190) located in the lower right corner of the cards (110) in thesefigures. Note that cards of the A(ce) rank may have either high or lowcosts and P/T/S attributes associated with them, depending on what theplayer who plays those cards chooses. The location of each card's cost(982, 184, 286, 788) and combat attributes, i.e. P/T/S (190), may varysomewhat due to space issues (see for example FIG. 5B), but will belocated at the bottom of the card when it is shown on the playing face(112) of the card (110). For reasons of space and because there are manyoptions for what combat attributes (190) or other features the MajorArcana cards (734, 735, 747) may have (described in more detail below),not all of the playing cards (110) will have a cost (184, 286, 788)shown on their playing faces (112).

FIGS. 2A and B illustrate the 2 of diamonds (FIG. 2A) and the 6 ofpentacles (FIG. 2B) playing cards (110). The UTM color indicator symbols(114) found in the upper left corner of these cards' (110) playing faces(112) have the standard RGB color green (220). Below the UTM colorindicator symbol (114) on these cards, we again find the poker card rank(130)—2, and the Minor Arcana card rank (132)—6, respectively. However,in FIGS. 2A and 2B, the rank color is R(eddish) (239). Rank colorR(eddish) (239) should not be confused with the standard RGB color red(118) as they indicate two different things. Standard RGB colors (516,118, 220, 322, 424, 626) indicate which one of 6 colors a card will beread as if a UTM is implemented within a game. Certain of the standardRGB colors (516, 118, 220, 322, 424) also indicate correspondencesbetween the poker suits (936) and the tarot suits (946). On the otherhand, rank color R(eddish) (239) and its complement, rank color B(lack)(137), serve as a way to divide the poker card ranks (130) and the MinorArcana card ranks (132) into two mixed rank decks with an equal numbersof playing cards (110) in each deck. These two decks will contain cardswhich have different P/T/S combat attributes (190) but shouldnonetheless be approximately equally matched when played against eachother. Rank color R (239) and rank color B (137) also serve to indicatewhich cards may be used when paying a playing card's (110) card cost(982,184, 286, 788) in games which require the payment of card costs(982,184, 286, 788) in order to play a card (110). Additionally, rankcolor R (239) and rank color B (137) carry over from standard 52 carddeck suit color (936, 138, 240, 342, 444) conventions, so leaving themunchanged enables variants of games which players may already befamiliar with to be created and played more easily.

Summarizing the elements introduced in FIGS. 2A and 2B which differ fromthose shown in FIG. 1, we have a new standard RGB color—green (220),rank color R (239), suit symbols for the poker suit diamonds (240) andthe Minor Arcana suit pentacles (250), and a card cost for rank color R(286) playing cards (110). Other elements and their general locations onthe playing faces (112) of the cards (110) illustrated should besomewhat familiar from a study of FIGS. 1A and 1B and the description ofthose illustrations above.

FIGS. 3A and 3B illustrate the 3 of hearts (FIG. 3A) and the 7 of cups(FIG. 3B). New elements introduced with these figures are as follows:standard RGB color aqua (322), the poker card suit hearts (342), and thetarot card suit cups (352). Once again, the positions of these and otherpreviously introduced elements should be familiar from a study of priorillustrations and their descriptions.

FIGS. 4A and 4B illustrate the 4 of spades (FIG. 4A) and the 8 of swords(FIG. 4B). Newly introduced elements on these figures are: standard RGBcolor yellow (424), the poker card suit symbol for spades (444), and thetarot card suit symbol for swords (454). The other elements and theirlocations on the playing faces (112) of these cards (110) have beenintroduced in previous figures and paragraphs.

FIGS. 5A and 5B introduce two cards from the tarot Minor Arcana with therank (132) C(hevalier). The chevalier or knight ranks above a jack butbelow a queen. Since in the English language the words knight and kingboth begin with the letter K, the French designation C(hevalier) forthis rank is used here instead. New elements introduced with these cardsare: standard RGB color blue (516) and the variable location of theP/T/S combat attributes (190) and card cost (982,184, 286, 788)indicators due to illustration (192) size and star name (176) length.Note also that the standard RGB color blue (516) is read for UTMpurposes for these cards, despite the additional presence of other (322,424) previously introduced UTM colors in the UTM color indicator symbols(114) on the playing faces (112) of these cards (110). This is becausefor the Rogozhin 4 state 6 color UTM we require 6 colors and only have 5natural suit divisions within the deck (once UTM color correspondencesbetween poker and tarot cards are assumed). Therefore, a 6th 22 card“royal” blue (516) colored division has been constructed from the K, Qand C card ranks (130, 132) and the B and R jokers (FIG. 6). For UTMpurposes, these cards fall into the standard RGB blue (516) category,but in other respects such as ranking the strength of different pokerhands and card costs (982,184, 286, 788) the UTM blue (516) playingcards (110) follow their suit, with the exception of the jokers, whichare described in more detail below. Note the numerical values (174) ofthe Arabic alphabet letters (170) associated with the cards illustratedin 5A and 5B as well, since these values (3 and 9, respectively) serveas a link between these two cards and the R joker (FIG. 6B) and B joker(FIG. 6A) respectively.

FIGS. 6A and 6B illustrate the B joker and R joker cards, whichintroduce a few new elements not seen in previous illustrations, butperhaps more importantly are different enough in various ways from therest of the playing cards (110) in the deck to merit full illustrations.As was mentioned previously in the description of FIG. 1A, the jokershave a different location on their playing faces (112) for their UTMstandard RGB color indicator symbols (114) from the rest of the playingcards (110) in the deck. Additionally, not mentioned previously, eachjoker has two of the UTM color symbols (114). This is to indicate thateach joker may take the suit of any card which shares its rank color(137, 239). Therefore, for purposes of a straight flush or a flush, theB joker (FIG. 6A) may be considered to be a club (138), a spade (444), awand (148), or a sword (454) as specified by the person who plays it atthe time it is put into play. Similarly, the R joker (FIG. 6B) may takeon the suits of diamonds (240), hearts (342), pentacles (250) and cups(352) as specified when it is played.

The introduction of one or more wildcards into a deck of playing cards(110) creates a paradox (EMERT and UMBACH) in terms of ranking therelative value of two poker hands based on the probability of beingdealt that hand from a well shuffled deck. One way to resolve thisparadox is to consider the jokers in a deck to be bug cards (HOYLE p.37) rather than full wildcards. Players should decide before any gamebegins how the jokers will function in the game. John Emert and DaleUmbach proposed another method of resolving the wild card paradox in anarticle in Chance magazine.

As mentioned in the description of FIGS. 5A and 5B, the jokers are readas standard RGB blue (516) color cards despite the presence of othercolors within their UTM color symbols (114). Also mentioned in thedescription of FIGS. 5A and 5B was to note the numerical values (174)associated with the Arabic alphabet letters (170) on the playing faces(112) of those two cards (110). Contained within the upside down wordjoker (130) on the playing faces (112) of the B joker (FIG. 6A) and theR joker (FIG. 6B) are the Greek alphabet letters (168) θ and γrespectively as well as their corresponding numerical values (174)—9 and3 respectively, although the number 3 is oriented so that it reads likethe letter E when the R joker (FIG. 6B) is turned upside down. Whenchoosing to consider the jokers in the deck as bugs, it is thereforerecommended that the default value of the B joker (FIG. 6A) be equal tothe C of swords (FIG. 5B) and that the default value of the R joker(FIG. 6B) be equal to the C of cups (FIG. 5A) unless the jokers are ableto complete a straight or a flush.

Finally, FIGS. 6A and 6B introduce 2 of the color/symbol instructionboxes (696) for Rogozhin's 4 state 6 color UTM. It should be noted thatthese UTM color/symbol instruction boxes (696) are included on theplaying faces (112) of their cards (110) to facilitate the operation ofone specific UTM without needing to refer to an instruction manual orother reference material outside the deck of cards itself. A moregeneralized embodiment of game components would likely not include theinstructions for one specific UTM, but rather allow for the possibilityof choosing from a selection of UTMs before the beginning of a game.However, given that there are 22 non halting UTM color/symbolinstruction boxes (696) and 22 Major Arcana cards (734) as well as twohalting UTM color/symbol instruction boxes (696) and two jokers (FIG. 6)assigning these specific instruction boxes (696) to the playing faces(112) of the cards (110) illustrated in this embodiment seemsappropriate.

With the introduction of the UTM color/symbol instruction boxes (696) onthe playing faces (112) of the cards (110) illustrated in FIG. 6 comesthe introduction of some new elements and symbols associated with theseUTM instruction boxes (696). The general layout of these instructionboxes (696) is to contain two boxes in a column with the upper boxcontaining a standard RGB color (118, 220, 322, 424, 516, 626) and amoon phase (897, 798, 699, 6100). In the case of a non halting UTMinstruction box (696), the lower box will contain a UTM color (118, 220,322, 424, 516, 626) and will have a moon phase (897, 798, 699, 6100)either to its left or to its right. In the case of a halting UTMinstruction box (696), both of which are illustrated in FIG. 6, therewill be identical colors (118, 220, 322, 424, 516, 626) and moon phases(897, 798, 699, 6100) in both upper and lower boxes and no moon phaseshown outside of one of the two boxes (6103), indicating neither a moveto the right or to the left, but rather a halt.

In summary, FIG. 6 introduces and illustrates the following newelements: different and multiple locations on the playing faces (112) ofthe cards (110) for the UTM color indicator (114), the concepts of wildcards and bugs in poker and the ranking paradox that wild cards cancreate, different locations and orientations for Greek alphabet letters(168) and their numerical values (174), and UTM color/symbol instructionboxes (696) along with their associated color (626), moon phases (699,6100), and halting instruction (6103).

FIGS. 7A and 7B introduce several new elements not seen in previousillustrations, since these figures are the first illustrations of theMajor Arcana or trump tarot suit (747) in the deck. In FIG. 6, thestandard RGB color magenta appeared within the illustrated UTMcolor/symbol instruction boxes (696), but FIG. 7A marks its firstappearance in an illustration within the UTM standard RGB colorindicator symbol (114). Also of note within the UTM color indicatorsymbol (114) is that both black and white background colors are usedwithin the same symbol (788). This dual background color use provides away of indicating that any predetermined Major Arcana card costs (788)may be paid with either rank color B (137) cards, rank color R (239)cards, or a combination of the two.

Mentioned in passing with the introductory description of card costs inthe description of FIGS. 1A and 1B was the fact that there are manyoptions for assigning P/T/S (190) and other potential attributes tocards in the Major Arcana suit (747). Many of these possibilities comefrom known prior art associations between combat or role playing gamesand tarot. A sampling of online search terms which yield relevant priorart includes:

-   -   “building a tarot deck from magic cards”    -   “Magic: the Gathering-like Tarot card game.”    -   “Tarot Combat: A Battle-Oriented Game Using A Tarot Deck”    -   “Deck of Many Things”    -   “Deck of Illusions”    -   “Are there any RPGs out there that use Tarot cards?”

Due to this large number of possible characteristics and attributes fora fairly limited number (22) of cards, selecting a reference sheet forthe costs, attributes and other aspects of the Major Arcana cards (747)before a game begins seems less limiting to the game variants playablewith these cards (110). The sites listed above provide examples for theconstruction of several sample reference sheets of this nature.

Continuing with a description of new elements introduced in FIGS. 7A and7B, we have, in descending order below the UTM color indicator symbol(114) the following elements: the Major Arcana card rank (734), thetarot trump suit symbol (747), and the first appearance of an I Chingelement (956) other than an I Ching hexagram (164)—in this case an IChing trigram (762). Below the I Ching trigram (762) we also find thenew elements of a Phoenician alphabet letter (772) and the first exampleof a planetary symbol (793). All of these newly introduced elements willhave similar locations on the playing faces (112) of the Major Arcana(734) playing cards (110) on which they occur. All of the Major Arcana(734) will have an associated trump suit card rank (734), Phoenicianalphabet letter (772), and trump card symbol (747). The tableillustrated in FIG. 9B provides a list of which Major Arcana cards (734)contain the other elements mentioned above (762, 164, 793). The elementintroduced in FIG. 7A which will have a consistent location on theplaying faces (112) of the Major Arcana cards (734) is the Major Arcanacard name (735). This will be located in the upper right corner of theplaying face (112) of the Major Arcana cards (734).

FIGS. 7A, 7B, 8A and 8B illustrate all of the cards in this embodimentwhich contain written or symbolic UTM instructions (7104, 7110) otherthan those contained within the previously introduced UTM color/symbolinstruction boxes (696). The written and symbolic UTM instruction set(7104) located across the bottom of the playing face (112) of the card(110) illustrated in FIG. 7A consists of the following elements: theTower symbol (7105),

, which is shown in various sizes and orientations, written text UTMrelated instructions (7110), arrow symbols (791) which indicate that theevent or symbol pointed at by the arrow is a forced next consequence ofwhat occurred prior to the arrow, and the Judgement symbol (7106), asilhouette of an angel blowing a trumpet, which calls for the writtenand symbolic UTM instruction set (7104) on the playing face (112) of theJudgement card (FIG. 7B) to be followed. The only other new elementintroduced in FIG. 7A is the move right instruction (7102) in the UTMcolor/symbol instruction box (696).

The playing face (112) of the Judgement card (FIG. 7B) introduces newelements which have not already been included in FIG. 7A or previousfigures: the 1st quarter moon symbol (798) and the move left instruction(7101) contained within the UTM color/symbol instruction box (696), theMuster illustration and instruction (7107) and the Inspectioninstruction which functions as the UTM read/write head (7111). For thosewho are unfamiliar with the orientation of the moon phases and maytherefore confuse the first quarter moon symbol (798) with the lastquarter moon symbol (6100), the following may be helpful. If the phasesof the moon are visualized on the face of a clock which has a fingerpointing out from its hour hand, the new moon phase, or state 1 (897),will be when the hour hand points to 12 o'clock, the first quarter moon,or state 2 (798), corresponds to 3 o'clock, the full moon, or state 3(699), corresponds to 6 o'clock and the last quarter moon, or state 4(6100), corresponds to 9 o'clock. The orientation and shape of the firstquarter moon (798) and last quarter moon (6100) resemble the fingernailon a finger pointing towards the corresponding hour on the clock. TheMuster illustration and instruction's (7107) function and purpose willbe described in detail later; visually it will be a small illustrationwhich represents a troop muster in combination with the word “Muster” toavoid any confusion about what the illustration symbolizes.

FIGS. 8A and 8B illustrate the playing faces (112) of the Major Arcanacards with the names (735) Death (FIG. 8A) and Justice (FIG. 8B) Theplaying face (112) of the Death card (FIG. 8A) introduces a few elementsnot shown in previous figures, namely: the UTM Death symbol (8108), askull and crossbones, and the new moon symbol contained within the UTMcolor/symbol instruction box (696). Additionally, on the playing face(112) of the Death card (FIG. 8A) we have the UTM halt instruction(8112) below the previously shown Muster illustration and instruction(7107), in this case written out verbally rather than indicatedsymbolically as before within UTM color/symbol instruction boxes (696).The only new element introduced on the playing face (112) of the Justicecard (FIG. 8B) is the Justice symbol (8109), which is a balance scale.

FIGS. 9A, 9B, and 9C are tables which illustrate how UTM color (516,118, 220, 322, 424, 626), I Ching line (956, 958, 960, 762, 164),alphabetic letter (168, 170, 772), stellar (176, 178, 180) and othersymbolic elements are assigned to playing cards (110) within the deckdescribed in this embodiment. Newly illustrated in the table shown inFIG. 9A is the general category of card cost (982) under which rankcolor B cost (184), rank color B (137), rank color R cost (286), andrank color R (239) elements are listed. Also new with FIG. 9A is ageneral category of card rank (928) which includes both poker card rank(130) and Minor Arcana card rank (132) below it. Suit P and Suit Tcategories are also new in this illustration and include beneath theirheadings the four poker card suits (138, 240, 342, 444) and the fourMinor Arcana card suits (148, 250, 352, 454). The last new headingillustrated in FIG. 9A is the I Ching line heading (956) under which wefind only I Ching hexagrams (164), but this heading is used again inFIG. 9B where it covers not only I Ching hexagrams (164) but also IChing lines (958), I Ching bigrams (960) and I Ching trigrams (762) aswell. These varying number of I Ching lines are the only elements whichare newly illustrated in FIG. 9B.

FIG. 9C is a table which shows, through the inclusion of Major Arcanacard ranks (734), B JO (FIG. 6A), and R JO (FIG. 6B) abbreviations, howeach one of the 24 color/symbol instruction boxes (696) of Rogozhin's 6color 4 state UTM are assigned to playing cards (110) in the deck. FIG.9C does not add any new elements not shown in prior figures.

Operation FIGS. 1A-9C

Hoyle's Rules of Games (Hoyle p. 1ff) makes up a subset of theoperational prior art for this embodiment, since it sets forth therules, customs, and popular variants for numerous 52 card deck cardgames. If some cards (110) in the deck are not used and the novelelements of this embodiment are ignored during play, it is possible toplay all card games which use only a standard 52 card deck. In oneoperational variant, I describe how Turing complete sets of 52 or 54cards may be constructed for playing Turing complete variations of thegames found in Hoyle's book, but in the other operational variants Iwill focus on operations, examples, and variants which use either theentire deck of playing cards (110) or a subset of the deck made up oftarot cards (132, 734, 735, 946, 747, 148, 250, 352, 454) in order tohighlight the novel elements of this embodiment.

A. Operational Variant 1—Solitaire Games Using Turing Complete TarotDecks

Instructions for playing variants of Klondike solitaire with 9 columnsusing both 2 standard decks and a tarot deck (SATIN, “How to play TarotSolitaire.”) have been published online, so creating a solitaire game orvariant which uses the entire deck in this embodiment should not poseinsurmountable problems. However, for simplicity we will consider knownsolitaire games using only a tarot deck in order to illustrate theoperations of this embodiment.

As a first example of games which may be adapted to be played using aTuring complete subset of the deck of playing cards (110) described inthis embodiment, we will look at solitaire games using tarot decks. “Howto play Tarot Solitaire” (SATIN) and “Wizard's Tower” (ROBINSON) providetwo different examples of solitaire variants which can be created andplayed with a tarot deck of 78 cards. All of the UTM instructionelements (696, 7104) except for those found on the jokers (FIGS. 6A and6B) are on the Major Arcana cards (734). We can see, therefore, that ifthe UTM instruction elements on the jokers (FIGS. 6A and 6B) areduplicated on their corresponding tarot cards (FIGS. 5B and 5A) thetarot portion of the deck (946) of playing cards (110) described in thisembodiment is Turing complete. This is the case because we may use thetarot portion (946) of the deck (if FIGS. 5B and 5A are modified toinclude UTM instructions) to simulate Rogozhin's 6 color 4 state UTM forany calculation requiring less than a predetermined length of time. Thisassumes that we have an ample supply of token markers of some type toperform the calculation. Token markers may take the form of 6 differentdenominations of coins (see FIG. 10), small pieces of different coloredpaper, or be represented with other readily available small objectswhich can correspond if necessary to the number of different UTM colors(516, 118, 220, 322, 424, 626) and states (897, 798, 699, 6100) requiredby whatever UTM is being simulated by a given embodiment. For a priorart reference to the use of tokens as a part of the simulation of a UTM,see CHURCHILL's “Magic Turing Machine v5”.

Players of solitaire games are likely familiar with end game situationsin which cards can be shifted around slightly without affecting theoutcome of the game. As an example, if one has a single red 3 which isplayed on one of two available black 4s, it is possible to move the 3from one 4 to the other, which in some games may affect the outcome, butin other endgame situations will make no difference in a lost gamesituation. With the addition of UTM elements into a card game, gamevariants are now available which in circumstances like this couldprovide an additional method of winning an otherwise unwinnable game orgame position with skillful play. One way this might be implemented isby assigning win/loss result outcomes to the two halt UTM color/symbolinstruction boxes (696) before beginning the game. In other words,declaring before the game “if a UTM run on the final state of this gamehalts in a R JO state, I win” and “if a UTM run on the final state ofthis game halts in a B JO state, I lose”. In a Turing complete deckconsisting only of tarot cards (946) as described above, we wouldsubstitute the corresponding C rank cards (FIG. 5) for the jokers (FIG.6) in the above statements, but the principle remains the same.

Thus, in solitaire positions where card movement or rearrangement isstill possible but any potential moves will not affect the outcome ofthe game, it becomes theoretically possible to calculate a game statewhich may be reached by rearranging the cards in a legal manneraccording to the rules of the game and then initiating a UTM on thefinal game position with the result of a UTM “declared” win as theoutcome. This may prove of interest in particular for otherwiseunwinnable initial deck conditions in popular solitaire games likeKlondike and Freecell.

In terms of operation of the UTM instruction elements (696, 7104) of theplaying cards (110), the tower symbol (7105)

on the playing face (112) of the Tower card (FIG. 7A) is what triggers asequence of forced steps which treat a game position as a tape to beread and adjusted as necessary by the read/write head of a UTM (7111).Raising the tower (as it applies to the phrase “

raiser” on the Tower card (FIG. 7A)) may take on a number of differentmeanings in the context of a solitaire game such as, for example, movingthe Tower card (FIG. 7A) during the course of the game or completing afoundation pile (HOYLE p. 194). Whatever definition is taken for raisingthe tower will affect the likelihood that a player is able to initiate aUTM should he or she desire to do so during a game. The phrase “At thebeginning of

raiser's next turn” as stated on the playing face (112) of the Towercard (FIG. 7A) is more easily understood in the context of games withmore than one player, but may be interpreted for solitaire purposes asmeaning the following: if the chosen meaning of a raised tower (

) or the phrase raising the tower has been met during the course of thegame, proceed to raze tower after a certain length of time when no moveshave occurred in the game. The sideways oriented tower symbol (7105) isthe symbol used to indicate the phrase “raze tower”. As mentionedpreviously, the arrow symbols (791) indicate that the event or symbolpointed at by the arrow occurs next as a forced consequence of whatoccurred prior to the arrow. Given the above interpretation of thephrases used in the written UTM instructions (7104) on the playing face(112) of the Tower card (FIG. 7A), raising the tower will trigger theactivation of the Judgement card UTM symbol (7106). The activation ofthe Judgement card UTM symbol (7106) in turn triggers the Muster UTMsymbol (7107) on the playing face (112) of the Judgement card (FIG. 7B)which in turn triggers the Inspection or read/write head instruction(7111).

The Muster symbol (7107) is designed to insure that all UTM instructionsare known or included in the equivalent of the Inspection read/writehead (7111) of the UTM being simulated. Practically, what this means inthis embodiment is that all 22 Major Arcana cards (734) and other cardswhich have UTM instruction elements (696, 7104) on their playing faces(112) have playing faces visible or readable for whoever or whatever ismanipulating the cards as the read/write head (7111) in the game. Thisread/write head manipulation may be incorporated as a part of a computerprogram running the game in some embodiments, but in other cases thiswill be one or more of the players. In some cases a neutral party notinvolved in the game may be called upon to perform this function.

The Inspection instruction (7111) is the initiation of the read/writehead on the initial state of the game in which it has been triggered.Players will need to decide before the game begins the game locationwhere the read/write head (7111) starts. For example, in the furthestaway, leftmost position of one's opponent's cards (110) as viewed by theUTM initiator might be one choice. In a solitaire game, a more likelychoice would be to initiate the read/write head with the nearest,leftmost card (110) in relation to the player. Once the read/write head(7111) is initiated, it follows the instructions for the UTM which isbeing simulated by the embodiment—in this case Rogozhin's 4 state, 6color UTM. The UTM instructions are found on the playing faces (112) ofthe Major Arcana cards (734) with the exception of the 2 haltinginstructions, as has been described previously.

Players of the game will need to decide before the beginning of the gamehow an empty space in the ranks of playing cards (110) is to beinterpreted. For this embodiment it is currently recommended that whenmoving right into a space not occupied by a card that the space be readas though it contained a standard RGB color blue card (516) in a newmoon or phase 1 state (897), or in other words to follow the UTMcolor/symbol instruction box (696) on the playing face (112) of MajorArcana card rank (734) V, Hierophant (735). When moving left into aspace not occupied by a card, it is currently recommended to considerthis empty space as though it contained a standard RGB color blue card(516) in a last quarter moon or phase 4 state (6100), or in other wordsto follow the UTM color/symbol instruction box (696) on the playing face(112) of Major Arcana card rank (734) XXI, World (735). Other optionsfor how the read/write head (7111) should interpret a blank space wouldlikely work as well, however.

Players will also need to decide before the beginning of a game themaximum length of time they wish for a potentially non halting UTM tapeto run before it is interrupted, since otherwise it could continue torun for an indefinitely long time and a game might never be completed.When this pre established upper limit is reached or when one of the haltinstructions (6103) on the playing faces (112) of the cards (110) isencountered, the Inspection instruction (7111) halts (8112). By thewritten/symbolic UTM instructions (7104) on the playing face (112) ofthe Death card (FIG. 8A), the halting (8112) of the Inspectioninstruction (7111) forces the UTM Death symbol (8108) to happen, whichsignifies the end of the game. The UTM Death symbol (8108) in turnforces the occurrence of the UTM Justice symbol, as indicated on theplaying face (112) of the Justice card (FIG. 8B). The Justice symboldetermines the winner of the game based on values assigned to differentUTM halting results before the beginning of the game.

Summarizing the operation of the UTM elements (696, 7104) as describedabove, we have the following: a player or players shall predetermine theconditions for how the UTM will function before beginning the game. Suchconditions include:

-   -   what game condition shall be required in order to “raise the        Tower” (7105) to initiate the UTM sequence (FIG. 7A) and whether        or not raising the Tower is mandatory if that condition is met    -   where the read/write head (7107) of the UTM simulator will begin        reading the layout of the playing cards (110) as well as overall        rules for the order in which the playing cards (110) are read in        a game position or layout    -   how the state of a given playing card (110) is indicated or        determined—for example this may be determined by the playing        card's (110) rotational orientation (right side up, rotated        clockwise 90 degrees from right side up, upside down and rotated        counterclockwise 90 degrees from right side up) or the position        of the card in the game layout (top card, 2nd card, third card,        and bottom card in a column of 4)    -   how the read/write head (7111) of the UTM simulator shall        interpret spaces which are not occupied by playing cards (110)        within the layout    -   how long a UTM will be allowed to run before it is halted if it        does not reach a halt instruction (6103) through reading the        layout of the playing cards (110) in the game    -   how halting conditions (6103) including a time limit halt shall        be interpreted in terms of whether the game has been won or lost        and by whom        Players will likely find preferred values for the above        mentioned initial game conditions after a few games and may then        use those values as default conditions. Once a game has been        started and the pre established condition for raising the Tower        (7105) has been met during the game, a player may choose to        raise the Tower (7105) or it may be required to happen due to        its game condition having been met. This depends on the initial        game conditions chosen. If or when the Tower is raised (7105)        during a game, that event triggers a series of forced events, as        follows:    -   1. raze the tower at the beginning of Tower raiser's next turn        (orient the Tower card (FIG. 7A) sideways to indicate this)    -   2. follow the UTM instructions (7104) on the playing face (112)        of the Judgement card (FIG. 7B)    -   3. the Muster symbol (7107) calls for all of the playing faces        (112) of cards containing UTM color/symbol instruction boxes        (696) to be in a visible location    -   4. the UTM color/symbol instruction boxes (696) instruct the UTM        read/write head (7111) what to do next based on the standard RGB        color and state of the playing card (112) being read    -   5. the Inspection instruction (7111) is the read/write head of        the UTM, which begins reading the game position based on the        initial game conditions chosen prior to the game    -   6. when the UTM halts (6103) due to initial game conditions of        time having been met or due to encountering a halt instruction        (6103) in a UTM color/symbol instruction box (696), a halting        (8112) of the read/write head of the UTM (7111) forces the Death        symbol (8108) on the playing face (112) of the Death card (FIG.        8 A) to occur, which ends the game    -   7. The Death symbol (8108) forces the Justice symbol (8109) on        the playing face (112) of the Justice card (FIG. 8B) to occur,        which determines the win/lose outcome of the game based on the        initial game conditions selected and what caused the UTM        read/write head (7107) to halt        Prior art which illustrates UTMs using color/symbol instruction        boxes (696) as shown in FIG. 9C may be found in A New Kind of        Science by S. Wolfram (p. 706ff). Therefore, operational details        for the UTM color/symbol instruction boxes (696) and the        elements contained within them (516, 118, 220, 322, 424, 626,        897, 798, 699, 6100, 7101, 7102, 6103) are assumed to be        explained sufficiently by prior art, since FIG. 9C alters the        colors and state symbols used by Wolfram but is equivalent in        terms of the illustration method.

Turing complete variations of solitaire games like Klondike (SATIN) andWizard's Tower (ROBINSON) use tarot cards, which have divinatorymeanings as well as prior art correspondences with other establisheddivination systems such as astrology (GRAY, E. pp. 209-25) and Hebrewalphabet letters through the Kabalah (GRAY, E. pp. 193-207). Turingcomplete full playing card (110) deck game operations which enable novelpossibilities for divinatory interpretations will be considered indetail later, but for the present we will consider divinatoryinterpretations in games using only tarot cards as being obviousextensions of the prior art.

Combat attributes—card power, toughness and speed (190) would be ignoredin the solitaire variants being considered and card costs (184, 286,788) would likely be ignored as well. However, some variants of Klondikesolitaire such as Las Vegas solitaire can be played for a score ordollar amount associated with each card played on a foundation.Incorporating somewhat different card costs (184, 286, 788) from thoseused in this embodiment for gambling or scoring purposes would be a wayto use card costs (184, 286, 788) in a solitaire game. See also FIG. 10for another example of how costs may be assigned to components within aTuring complete game.

In summary, the novel operational elements of Turing complete solitairevariants which use only tarot cards are:

-   -   predetermined rules regarding UTM outcomes, instructions, and        initiation    -   the operation of the UTM instructions (7104) on the playing        faces (112) of the cards in FIGS. 7A, 7B, 8A and 8B    -   the potential for winning otherwise unwinnable solitaire games        by initiating a UTM    -   novel possibilities for gambling/scoring point systems based        around card cost variations (982, 184, 286, 788)

B. Operational Variant 2—Two Player Combat Games Using Turing CompleteCard Decks

Prior art examples of combat style games using both tarot decks andstandard card decks including “Magic 1513: Tarot Combat II” (GRAY, J.)and “Playing Card Magic” (ROBINSON) have been mentioned previously.Playing a Turing complete variant of a two player combat game like TarotCombat II is operationally fairly similar to playing a Turing completetarot solitaire game as described above. Elements in this embodiment notused in solitaire games will be included in Turing complete two playercombat games using standard playing cards as well as those using tarotcards. Therefore, in this variant we will discuss a Turing completestandard 54 card deck modified for Turing completeness as follows:

-   -   2-10        are standard RGB color red (118)    -   2-10        are standard RGB color green (220)    -   2-10        are standard RGB color aqua (322)    -   2-10        are standard RGB color yellow (424)    -   A,K,Q,J of rank color R (239) suits+R JO are standard RGB color        magenta (626)    -   A,K,Q,J of rank color B (137) suits+B JO are standard RGB color        blue (516)    -   the UTM color/symbol instruction boxes (696) are included on the        playing faces (112) of the 9-A of all four suits, with the R JO        and B JO (FIG. 6) instructions assigned to the one eyed Jacks        (HOYLE, p. 261), other instructions may be assigned in ascending        rank and bridge suit order (HOYLE p. 2) or in other ways    -   the written/symbolic UTM instructions (7104) on the playing        faces (112) of the cards illustrated in FIGS. 7 and 8 may be        assigned to cards in various ways including to the four aces,        the four nines or as they seem to fit the cards symbolically

The cards in this alternate embodiment may additionally have all of theassociated divinatory elements (956, 168, 170, 772, 973, 174, 176, 178,180), combat attributes (190), and card costs (184, 286) illustrated inFIG. 9A. Using a modified standard playing card deck such as describedabove, it is easy to construct Turing complete 2 player combat gameswith divinatory elements based on prior art game rules like “Combat: ABattle-Oriented Card Game” (GRAY, J.) and “Playing Card Magic”(ROBINSON). In addition to the operations described in Operationalvariant A above, a two player combat game adds:

-   -   turns and turn numbers which can correspond to lunar mansions        (180) within a game; these in turn may change a playing card's        (110) UTM state (897, 798, 699, 6100) or combat attributes (190)    -   a card cost (982, 184, 286) use besides the above mentioned        scorekeeping or gambling uses, as described in the prior art    -   a game use for combat attributes (190) as described in the prior        art

Since we are now looking at a standard playing card deck plus jokers asthe basic deck in the game, it's worth highlighting something mentionedin the description of the game “Playing Card Magic” (ROBINSON). With a52 card deck, there are 78 non pair combinations of cards if suits areignored. This offers the potential for a game variant based around twocard combinations having the potential to be melded together to createdifferent spells, each of which could be represented by one of the 78different cards in a tarot deck. Therefore, a 54 card deck game coulduse a tarot deck as a “spellbook”. Tarot cards, in particular the MajorArcana (734, 735) cards have various prior art uses, associations, andcorrespondences with combat game cards and role playing games, asmentioned previously. The assigning of two poker deck card combinationsto a given tarot card may be done in different ways and there are manypotential game uses for the resulting tarot cards which will be coveredin more detail later.

In summary, Turing complete versions of prior art two player combatgames are operationally similar to Turing complete tarot solitairevariants, but allow for additional playing card (110) elements to beincorporated, including UTM states (897, 798, 699, 6100) and lunarmansions (180) based on the current turn number in the game, combatattributes (190) which may fluctuate based on turn based timekeeping andlunar mansions (180), card costs (982, 184, 286), and spells andtransformations based on combining two unpaired poker cards andassigning that combination a corresponding tarot card.

C. Operational Variant 3—Turing Complete Battle Line/Combat Tarot HybridVariants

Thirdly, we look at additional elements not covered in previousvariants, such as planetary symbols (793) and how wildcards (FIG. 6) andpoker hand rank may be added as elements in a two player combat game.For this, we turn to the prior art game example of GMT Games' “BattleLine”, its Terrain card expansion (FORSLUND) and a prior art variant(SALANDER). Comparing and contrasting Battle Line with the Turingcomplete tarot deck described in Operational variant 1, we have:

-   -   tarot deck=4 different UTM colored suits (118, 220, 322, 424) of        11 cards each+1 UTM colored suit (516) of 12 cards and one UTM        colored suit (626) of 22 cards—9 of which have planetary symbols        (793) on them—for a total of 78 cards    -   Battle Line with Terrain cards=6 colors of 10 cards each for        troop cards+10 tactic cards+9 terrain cards (FORSLUND) for a        total of 79 cards        The terrain and tactic portions of the Battle Line terrain deck        have some close and rough correspondences with some of the Major        Arcana (734, 735) cards including TOWER and Tower (FIG. 7A),        Alexander/Darius (Emperor/Empress or Emperor/Hierophant), but        perhaps more importantly are some close name and elemental        parallels between the 9 terrain cards and the 8 trigrams of the        I Ching (LEE) which are associated with Major Arcana cards (734,        735) which have planetary symbols (793) on their playing faces        (112).

Given that several Battle Line tactic cards have wildcard or bug cardsimilarities, that terrain cards are captured based on poker hand ranksand coincide well with Major Arcana (734, 735) cards, thecorrespondences between poker card ranks (130) and the Minor Arcana(132) card ranks and the similarities of card numbers and colors betweena tarot deck and a Terrain expansion Battle Line deck, creating a closevariant to Battle Line using a Turing complete Tarot deck does notappear to present insurmountable challenges. However, since some type ofCombat Tarot/Battle Line with terrain expansion hybrid variant appearsmost readily to cover all of the elements of the playing cards (110) inthis embodiment, I suggest hybrid variants of this type as the currentlypreferred type of game variant for a Turing complete tarot deck. ATuring complete tarot deck variant similar to “Battle Line—AncientBattles” (SALANDER), for example, could incorporate card costs (184,286, 788) using the point system described for that variant, use thecard costs (184, 286, 788) in a manner similar to that used for “Magic1513: Tarot Combat II” (GRAY, J.) or use them in a way similar to howcard costs may be used in a gambling variant of Klondike solitaire asdescribed in operational variant A Major Arcana (734, 735) cards withplanetary symbols (793) on their playing faces (112) could be adapted tofunction as terrain cards based on their I Ching line (958, 762)interpretations. UTM states (897, 798, 699, 6100) and lunar mansions(180) would be calculated within the game based on the number of turnswhich had happened in the game, with one method described as follows:turns 4-10=UTM state 2 (798), turns 11-17 state 3 (699), turns 18-24state 4 (6100), turns 25,26,27,28,1,2,3 state 1 (897), turns above the29th turn have multiples of 28 subtracted from them as needed in orderto have a turn number between 1 and 28. If a turn number is equal to alunar mansion (180) number on the playing face (112) of a card (110),this gives a +1 bonus to a chosen combat attribute (190) of that card(110) at any time during that turn. Other operational elements may behandled as described in operational variant A.

With the addition of the poker cards (130, 138, 240, 342, 444, FIG. 6)to the tarot cards (132, 734,735, 747, 148, 250, 352, 454), nosignificant operational elements are added, however this addition allowsfor the possibility of each player having a deck of 55 cards, all of thesame rank color (137, 239) to draw cards from and thus enables thepossibility of constructing 5 or 6 card poker hands to compete againsteach other for terrain cards in a Battle Line variant. Also, if the twojokers (FIG. 6) are only allowed to vary between one or the other of theC cards (FIG. 5) corresponding to their rank color (137, 239) theplaying strength of the poker cards (130, 138, 240, 342, 444, FIG. 6)and the Minor Arcana (132, 148, 250, 352, 454, FIG. 5) cards should besimilar enough to allow competitive games to be played pitting those twodecks against each other.

Mentioned in passing previously was the fact that if a game variantallows the combining or melding of two poker cards of different ranks(130) in order to form a single tarot card (132, 734, 735) according toa predetermined list of which combination yields which card, then theresulting tarot card (132, 734, 735) might have a variety ofinterpretations, depending on the rules of the game being played. In afull deck of playing cards (110) combining a poker deck (130, 138, 240,342, 444, FIG. 6) and a tarot deck (132, 734, 735, 946, 747, 148, 250,352, 454) as described in this embodiment, pairing of otherwise uniqueplaying cards (110) in the deck, such as the Major Arcana (734, 735)could be achieved through the combining of poker cards. This type of usewould require some additional hand ranking charts beyond those typicallyused for poker style games, but this would likely just be a matter ofextending the hierarchy of pairs above Aces to include the Major Arcanacards (734, 735). Duplicated Minor Arcana (132) cards could be treatedsimply as pairs, or in the case of ties a pair of cards of the same rank(132) which included a card duplicated by combining two poker cards(130) could beat an ordinary pair of the same rank (132). Alternativeuses for tarot cards (132, 734, 735) created by melding two poker cards(130) include spells (as covered previously) and as wildcards for suitvalues, where a card of rank 2 created in this way could take any suit,depending on the preference of the player making the meld.

Finally, a few practical notes touching on the physical operation of theUTM read/write head (7107) during games played with physical (as opposedto virtually simulated) playing cards. Multi colored paper clips arelikely to be a good choice for easily and temporarily marking changesmade by the UTM read/write head (7107). Attaching a paper clip of asimilar color to the UTM color (516, 118, 220, 322, 424, 626) which aplaying card (110) is being changed to by the UTM read/write head (7107)on the top, right side, bottom, or left side of the card could be a wayto indicate that playing card's (110) current UTM color (516, 118, 220,322, 424, 626) and state (897, 798, 699, 6100). Also, note that the UTMread/write head when it moves left or right according to the playingcard (110) it has just read may find itself reading a blank spacedespite the previous card having neighboring playing cards (110) to itsleft and right. This is due to the state change of the UTM read/writehead (7107). Each playing card (110) in a game layout can be consideredto be in one of 4 states in the current embodiment. If the state of aplaying card (110) does not match the state of the UTM read/write head(7107) when it moves to the left or right, that card is ignored by theread/write head (7107) and a token card is placed above or below thatcard, depending on the state of the read/write head (7107) and theplaying card (110) in relationship to each other. What the state andcolor of a particular token card are has been predetermined before thegame begins, as discussed previously. The token card is then read andwritten over by the read/write head (7107) and the process continuesuntil a halt situation is reached.

DETAILED DESCRIPTION FIG. 10-Second Embodiment

FIG. 10 illustrates two dimensional symbolic representations of chesspieces (1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038,1040) on the playing surface (1012) of a chessboard (1010) in theirstarting positions for a chess game (HOYLE p. 214). A standard RGB color(516, 118, 220, 323, 424, 626) has been assigned to all of the pawns(1030, 1042), knights (1022, 1034), bishops (1024, 1036), rooks (1020,1032), kings (1026, 1038) and queens (1028, 1040) disregarding whichside of the game they are playing on. In two dimensional symbolic form,each piece has a distinguishable right side up and upside downorientation and may also be rotated 90 or 270 degrees clockwise toindicate that it is in one of four possible states or phases, in asimilar manner to the previously described first embodiment. We mayenvision these symbolic chess pieces (1020, 1022, 1024, 1026, 1028,1030, 1032, 1034, 1036, 1038, 1040) as having been drawn on squarepieces of transparent film, along with elements from the firstembodiment (130, 734, 168, 170, 180, 696, 897, 798, 699, 6100, 7101,7102, 6103). In this way, the transparent film squares can be seen as a32 card deck of cards which contain many of the elements from the firstembodiment. An I Ching hexagram (164) may easily be assigned to eachsquare (1014, 1016) of the chessboard (1010) in an obvious way, since IChing hexagrams are frequently illustrated in an 8 by 8 square gridpattern. Two different I Ching hexagrams (164) may be assigned to eachchess piece (1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038,1040). The first I Ching hexagram (164) would be written on the obverseside of the square piece of film and would be determined by the I Chinghexagram (164) which corresponds to that chess piece's (1020, 1022,1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038, 1040) initial position.The second hexagram (164) would be written on the reverse side of thefilm and would correspond to the hexagram (164) of the chessboard (1010)square (1014, 1016) two rows closer to the center of the chessboard(1010) than that chess piece's (1020, 1022, 1024, 1026, 1028, 1030,1032, 1034, 1036, 1038, 1040) initial position. If pre game UTMconditions for a Turing complete chess game are established in a similarway to that described in the Operational variant 1 section of the firstembodiment, Turing complete variants of chess may be played within afinite surface area or volume of space. One or more UTM initiatingconditions like the one (7105) described in the first embodiment may beselected before the game begins from rare or common events within atypical chess game, for example:

-   -   if a player promotes a pawn to a rook (HOYLE, p. 217), initiate        a UTM reading of the game    -   if a player captures en passant (HOYLE, p. 216), initiate a UTM        reading of the game    -   if a player castles (HOYLE, p. 217) queenside (or kingside),        initiate a UTM reading of the game    -   if the threefold repetition rule (HOYLE, p. 218) can be invoked        in a game, a player may instead initiate a UTM reading of the        game

One final note about this embodiment is that different denominations ofcoins or currency may also be used to represent the chess piecesdescribed in this embodiment. Money may also be used for token piecesput on the board as required by a UTM reading of the game. This offersthe potential for gambling within a Turing complete variant of chess ina manner which could theoretically be skill based. For example, if I cansee that a high percentage of my opponent's legal next moves wouldresult in a UTM win for me if a Turing machine reading of the game isinitiated, and we are playing a Turing complete chess variant in whichthe winner of the game keeps any money put onto the board during thegame, then I could gamble that my opponent would not be able to find awinning next move and that therefore the odds would be in my favor if Iinitiated a UTM.

Additional Embodiments

Many other Turing complete game embodiments are possible, but I willgive just two more brief descriptive examples to illustrate some otherpossibilities for adapting games to be played as Turing completevariants and then discuss ramifications. Games like Gomoku (SCARNE, p.537) and Go (SCARNE, pp. 533-7) which are played on a 19×19 grid withtwo different colors of pieces are also candidates for Turing completevariants with divinatory elements. In the case of these games,Rogozhin's (2,18) UTM is used. This is also the UTM used by Churchill(2012) as cited in the prior art references. In order to create a gamevariant of this type, we will use coins for our game pieces. Prepare toplay the chosen game variant by sorting large quantities of twodifferent coins—pennies and dimes for example—into piles based on thedate on their obverse sides. In this case, dates on the coins will beused as a substitute for colors in the context of the UTM instructions.Colors have been used for UTM instructions in the previously describedembodiments, but this embodiment illustrates that another attribute ofthe game components, in this case a number, may be used. In the mostgeneral case, I will refer to this potential for substituting anotherattribute of the game components in place of colors as a use of a subsetof the set of game components. Each player should start with 19 stacksof 19 of their chosen coin. Each stack of pennies and dimes shouldcontain only coins with the same date—let's say, for example, 19 penniesdated 1991, 19 dimes dated 1991, 19 pennies dated 1992, etc. through 19dimes dated 2009. A coin may only be played in the leftmost column ofthe board if it has a 1991 date, the next column to the right requires acoin with the 1992 date, etc. through to 2009 in the rightmost column.Play a game of Go or Gomoku as normal except for this rule regardingwhich pieces may be played where. When the (2,18) UTM is initiated basedon pre selected game criteria (in a similar manner to that described inother embodiments) the UTM read/write head will read a heads up coin asbeing in state 1 and a heads down coin as being in state 2. A coin withthe date 1991 will be considered an A coin by the UTM, 1992=B, 1993=C,etc. skipping over the year 2000. Coins are replaced by others withdifferent dates according to the UTM instructions. As far as divinatoryelements are concerned, there are 360 degrees in the zodiac and 360intersections surrounding the central intersection on a Go board, soSabian symbols (ROCHE) are an obvious fit. For more divinatory aspectsof a Go board and game, see “The Religious Dimensions of Go”(SCHNEIDER).

As a final example of an additional form an embodiment could take, Irefer readers to the illustration for U.S. Pat. No. 214,048, which shows36 equilateral triangles arranged to form 6 hexagrams which surround a 6pointed star. Each of the 36 equilateral triangles in the illustrationis divided into three smaller triangles and has a number of dots placedalong each of its sides. The number of dots range between 1 and 6. Ifthe dots are taken to indicate one of the 6 UTM colors (516, 118, 220,322, 424, 626), then each small triangle may be colored according to thenumber of dots within it. If these three colored triangles within anequilateral triangle are interpreted as being three visible faces of atetrahedron as viewed from above, then we have a pattern for a variantof the game described in U.S. Pat. No. 214,048 which would use a numberof tetrahedral dice, which could have one of 6 different UTM colors(516, 118, 220, 322, 424, 626) on each face and 4 faces which couldcorrespond to states in the UTM illustrated in FIG. 9C.

CONCLUSIONS, RAMIFICATIONS, AND SCOPE

Accordingly, the reader will see that designed sets of Turing completegame components in various embodiments allow for the playing of Turingcomplete two player tabletop games, afford a simpler way to simulate aTuring machine in a tabletop game than has been demonstrated in theprior art, and the ability to initiate a Turing machine calculation on agame state adds an additional strategic factor to games.

The first embodiment in particular has ramifications for cryptography,since it includes three complete alphabets on the playing faces (112) ofthe cards (110) and an encryption method using a standard 52 card deckplus jokers exists in the prior art. See “The Solitaire EncryptionAlgorithm” by Bruce Schneier as featured in Neal Stephenson's bookCryptonomicon for further details on using a deck of cards forencryption purposes. The potential for ramifications involving gamblingon deterministic rather than chance outcomes has been mentioned for thedifferent embodiments covered, and it can be used for games with eitherperfect information or imperfect information. Having the option toimplement a Turing machine during a game can also provide a method forwinning otherwise unwinnable game as was mentioned in the case ofsolitaire. This could also have ramifications for game which havepositions considered as draws in their non Turing complete forms, forexample checkers, chess, and shogi. Many other games in the prior artare good candidates for Turing complete variations with divinatoryelements, including but not limited to: Checkers, Chinese Checkers,Bridge (including 5 and 6 suit prior art variants of Bridge), Pinochle,and Dominoes. In some cases, it may be preferable to simulate auniversal Turing machine for a finite maximum number of steps ratherthan a finite period of time.

I claim:
 1. Manufactured sets of game components comprising: a. aplurality of game components with a plurality of attributes associatedwith each of said game components, including a plurality of distinctcolors or subsets within each set of game components; and b. said gamecomponents shall additionally have a plurality of distinct states ororientations which they may take during a game; and c. the distinctcolors and states of each set of game components shall be at least equalin number to the number of colors and states in a Turing machine whichhas been proven to be universal; and d. a set of instructions whereby,when the instructions are applied to the colors and states of said gamecomponents as they are arrayed within a finite playing area during agame, said set of instructions will cause the reader of said set ofinstructions to simulate the operation of a universal Turing machine fora finite period of time, the maximum length of said period of time beingpredetermined before the game begins.
 2. The manufactured sets of gamecomponents of claim 1 wherein a plurality of said game components haveat least one divinatory element written upon, inscribed on, affixed to,or otherwise associated with each of said game components; and a. someof said divinatory elements may temporarily alter at least one of theattributes of its associated game component during a game; and b. achange in the state or orientation of said game components may changehow some of said divinatory elements are interpreted.